Norm constants in cases of the Caffarelli-Kohn-Nirenberg Inequality

Akshay L. Chanillo; Sagun Chanillo; Ali Maalaoui

doi:10.2140/pjm.2018.292.293

Norm constants in cases of the Caffarelli-Kohn-Nirenberg Inequality

Akshay L. Chanillo, Sagun Chanillo, Ali Maalaoui

SAS - Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Based on elementary linear algebra, we provide radically simplified proofs using quasiconformal changes of variables to obtain sharp constants and optimizers in cases of the Caffarelli-Kohn-Nirenberg inequality. Some of our results were obtained earlier by Lam and Lu.

Original language	English (US)
Pages (from-to)	293-303
Number of pages	11
Journal	Pacific Journal of Mathematics
Volume	292
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2018.292.293
State	Published - 2018

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Caffarelli-Kohn-Nirenberg inequality
Optimizers
Quasiconformal maps
Sharp constants
Weighted Sobolev inequality

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title = "Norm constants in cases of the Caffarelli-Kohn-Nirenberg Inequality",

abstract = "Based on elementary linear algebra, we provide radically simplified proofs using quasiconformal changes of variables to obtain sharp constants and optimizers in cases of the Caffarelli-Kohn-Nirenberg inequality. Some of our results were obtained earlier by Lam and Lu.",

keywords = "Caffarelli-Kohn-Nirenberg inequality, Optimizers, Quasiconformal maps, Sharp constants, Weighted Sobolev inequality",

author = "Chanillo, {Akshay L.} and Sagun Chanillo and Ali Maalaoui",

note = "Funding Information: S. Chanillo was supported in part by NSF grant DMS-1201474 Publisher Copyright: {\textcopyright} 2018 Mathematical Sciences Publishers.",

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language = "English (US)",

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T1 - Norm constants in cases of the Caffarelli-Kohn-Nirenberg Inequality

AU - Chanillo, Akshay L.

AU - Chanillo, Sagun

AU - Maalaoui, Ali

PY - 2018

Y1 - 2018

N2 - Based on elementary linear algebra, we provide radically simplified proofs using quasiconformal changes of variables to obtain sharp constants and optimizers in cases of the Caffarelli-Kohn-Nirenberg inequality. Some of our results were obtained earlier by Lam and Lu.

AB - Based on elementary linear algebra, we provide radically simplified proofs using quasiconformal changes of variables to obtain sharp constants and optimizers in cases of the Caffarelli-Kohn-Nirenberg inequality. Some of our results were obtained earlier by Lam and Lu.

KW - Caffarelli-Kohn-Nirenberg inequality

KW - Optimizers

KW - Quasiconformal maps

KW - Sharp constants

KW - Weighted Sobolev inequality

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JF - Pacific Journal of Mathematics

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ER -

Norm constants in cases of the Caffarelli-Kohn-Nirenberg Inequality

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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